Quasi-topological spaces today seem to be regarded mostly as a historical curiosity, perhaps because working topologists were never comfortable with the set-theoretic issues that accompany them. In retrospect, however, they are an impressive testament to the conceptual insight of Spanier into ideas of topos theory which were at the time (early 1960’s) barely in the air, and even not quite born yet (being an early example of quasitopos, whose name perhaps derives from Spanier’s notion).